• Home
  • Analytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems
  • Author : A.S. Yakimov
  • Publsiher : Academic Press
  • Release : 13 August 2016
  • ISBN : 0128043636
  • Pages : 200 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKAnalytical Solution Methods for Boundary Value Problems

Summary:
Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content


Analytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems
  • Author : A.S. Yakimov
  • Publisher : Academic Press
  • Release : 13 August 2016
GET THIS BOOKAnalytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential


Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

Solving Ordinary and Partial Boundary Value Problems in Science and Engineering
  • Author : Karel Rektorys
  • Publisher : CRC Press
  • Release : 20 October 1998
GET THIS BOOKSolving Ordinary and Partial Boundary Value Problems in Science and Engineering

This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating


Boundary Value Problems for Engineers

Boundary Value Problems for Engineers
  • Author : Ali Ümit Keskin
  • Publisher : Springer
  • Release : 19 June 2019
GET THIS BOOKBoundary Value Problems for Engineers

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist


Spline Solutions of Higher Order Boundary Value Problems

Spline Solutions of Higher Order Boundary Value Problems
  • Author : Parcha Kalyani
  • Publisher : GRIN Verlag
  • Release : 09 June 2020
GET THIS BOOKSpline Solutions of Higher Order Boundary Value Problems

Doctoral Thesis / Dissertation from the year 2014 in the subject Mathematics - Applied Mathematics, , language: English, abstract: Some of the problems of real world phenomena can be described by differential equations involving the ordinary or partial derivatives with some initial or boundary conditions. To interpret the physical behavior of the problem it is necessary to know the solution of the differential equation. Unfortunately, it is not possible to solve some of the differential equations whether they are ordinary or partial with


Numerical-Analytic Methods in the Theory of Boundary-Value Problems

Numerical-Analytic Methods in the Theory of Boundary-Value Problems
  • Author : M Ronto,A M Samoilenko
  • Publisher : World Scientific
  • Release : 30 June 2000
GET THIS BOOKNumerical-Analytic Methods in the Theory of Boundary-Value Problems

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs. The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with


Numerical Boundary Value ODEs

Numerical Boundary Value ODEs
  • Author : Ascher,Russell
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKNumerical Boundary Value ODEs

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to




Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
  • Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
  • Publisher : SIAM
  • Release : 01 December 1994
GET THIS BOOKNumerical Solution of Boundary Value Problems for Ordinary Differential Equations

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one


Finite Difference Methods. Theory and Applications

Finite Difference Methods. Theory and Applications
  • Author : Ivan Dimov,István Faragó,Lubin Vulkov
  • Publisher : Springer
  • Release : 28 January 2019
GET THIS BOOKFinite Difference Methods. Theory and Applications

This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.


Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field

Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field
  • Author : Gehan Anthonys
  • Publisher : Morgan & Claypool Publishers
  • Release : 01 February 2018
GET THIS BOOKAnalytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field

The investigation of the behavior of ferromagnetic particles in an external magnetic field is important for use in a wide range of applications in magnetostatics problems, from biomedicine to engineering. To the best of the author's knowledge, the systematic analysis for this kind of investigation is not available in the current literature. Therefore, this book contributes a complete solution for investigating the behavior of two ferromagnetic spherical particles, immersed in a uniform magnetic field, by obtaining exact mathematical models on



Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics

Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics
  • Author : N E Tovmasyan
  • Publisher : World Scientific
  • Release : 08 February 1994
GET THIS BOOKBoundary Value Problems for Partial Differential Equations and Applications in Electrodynamics

The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed. A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to


Iterative Methods for the Numerical Solutions of Boundary Value Problems

Iterative Methods for the Numerical Solutions of Boundary Value Problems
  • Author : Mariam B. H. Abushammala
  • Publisher : Anonim
  • Release : 08 March 2021
GET THIS BOOKIterative Methods for the Numerical Solutions of Boundary Value Problems

"The aim of this thesis is twofold. First of all, in Chapters 1 and 2, we review the well-known Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) for obtaining exact and numerical solutions for ordinary differential equations, partial differential equations, integral equations, integro-differential equations, delay differential equations, and algebraic equations in addition to calculus of variations problems. These schemes yield highly accurate solutions. However, local convergence is a main setback of such approaches. It means that the accuracy deteriorates as the


Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations
  • Author : Martin Hermann,Masoud Saravi
  • Publisher : Springer
  • Release : 09 May 2016
GET THIS BOOKNonlinear Ordinary Differential Equations

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical